•
Journal of Micromechanics and Microengineering (JMM): a peer-
reviewed scientific journal published by the Institute of Physics of Bristol,
United Kingdom.
•
Sensors Magazine: a trade journal with emphasis on practical and commercial
applications. It is published by Helmers Publishing, Inc., of Peterborough,
New Hampshire.
•
MST News: a newsletter on microsystems and MEMS. It is published by
VDI/VDE Technologiezentrum Informationstechnik GmbH of Teltow, Ger-
many, and is available on-line.
•
Micro/Nano Newsletter: a publication companion to “R&D Magazine”
with news and updates on micromachined devices and nanoscale-level
technologies. It is published by Reed Business Information of Morris Plains,
New Jersey.
•
Small Times Magazine: a trade journal reporting on MEMS, MST, and nano
-
technology. It is published by Small Times Media, LLC, a subsidiary company
of Ardesta, LLC, of Ann Arbor, Michigan.
List of Conferences and Meetings
Several conferences cover advances in MEMS or incorporate program sessions on
micromachined sensors and actuators. The following list gives a few examples:
•
International Conference on Solid-State Sensors and Actuators (Transducers):
held in odd years and rotates sequentially between North America, Asia, and
Europe.
•
Solid-State Sensor and Actuator Workshop (Hilton-Head): held in even years

www.atip.org
•
Micro Electro Mechanical Systems Workshop (MEMS): an international
meeting held annually and sponsored by the IEEE.
•
International Society for Optical Engineering (SPIE): regular conferences
held in the United States and sponsored by SPIE of Bellingham, Washington.
•
Micro Total Analysis Systems (µTAS): a conference focusing on microanalyti
-
cal and chemical systems. It is an annual meeting and alternates between
North America and Europe.
Summary
Microelectromechanical structures and systems are miniature devices that enable the
operation of complex systems. They exist today in many environments, espe
-
cially automotive, medical, consumer, industrial, and aerospace. Their potential for
future penetration into a broad range of applications is real, supported by strong
development activities at many companies and institutions. The technology consists
of a large portfolio of design and fabrication processes (a toolbox), many borrowed
from the integrated circuit industry. The development of MEMS is inherently inter
-
disciplinary, necessitating an understanding of the toolbox as well as of the end
application.
References
[1] Dr. Albert Pisano, in presentation material distributed by the U.S. DARPA, available at
.
[2] System Planning Corporation, “Microelectromechanical Systems (MEMS): An SPC Market
Study,” January 1999, 1429 North Quincy Street, Arlington, VA 22207.
[3] Frost and Sullivan, “World Sensors Market: Strategic Analysis,” Report 5509-32, February

Petersen, K. E., “Silicon As a Mechanical Material,” Proceedings of the IEEE, Vol. 70,
No. 5, May 1982, pp. 420–457.
12 MEMS: A Technology from Lilliput
CHAPTER 2
Materials for MEMS
“You can’t see it, but it’s everywhere you go.”
—Bridget Booher, journalist, on silicon
If we view micromachining technology as a set of generic tools, then there is no rea
-
son to limit its use to one material. Indeed, micromachining has been demonstrated
using silicon, glass, ceramics, polymers, and compound semiconductors made of
group III and V elements, as well as a variety of metals including titanium and tung
-
sten. Silicon, however, remains the material of choice for microelectromechanical
systems. Unquestionably, this popularity arises from the large momentum of the
electronic integrated circuit industry and the derived economic benefits, not least of
which is the extensive industrial infrastructure. The object of this chapter is to pres
-
ent the properties of silicon and several other materials, while emphasizing that the
final choice of materials is determined by the type of application and economics.
Silicon-Compatible Material System
The silicon-compatible material system encompasses, in addition to silicon itself, a
host of materials commonly used in the semiconductor integrated circuit industry.
Normally deposited as thin films, they include silicon oxides, silicon nitrides, and
silicon carbides, metals such as aluminum, titanium, tungsten, and copper, and
polymers such as photoresist and polyimide.
Silicon
Silicon is one of very few materials that is economically manufactured in single-
crystal substrates. This crystalline nature provides significant electrical and
mechanical advantages. The precise modulation of silicon’s electrical conductivity

solutions (see Figure 2.1). Silicon has a diamond-cubic crystal structure that can be
14 Materials for MEMS
Table 2.1 Properties of Selected Materials
Property
a
Si SiO
2
Si
3
N
4
Quartz SiC Diamond GaAs AlN 92%
Al
2
O
3
Polyimide PMMA
Relative
permittivity (ε
r
)
11.7 3.9 4–8 3.75 9.7 5.7 13.1 8.5 9 — —
Dielectric
strength
(V/cm ×10
6
)
0.3 5–10 5–10 25–40 4 10 0.35 13 11.6 1.5–3 0.17
Electron
mobility

(W/m·K)
157 1.4 19 1.4 500 990–2,000 0.46 160 36 0.12 0.2
Specific heat
(J/g·K)
0.7 1.0 0.7 0.787 0.8 0.6 0.35 0.71 0.8 1.09 1.5
Melting
temperature (ºC)
1,415 1,700 1,800 1,610 1,800
b
3,652
b
1,237 2,470 1,800 380
c
90
c
a
Properties can vary with crystal direction, crystal structure, and grain size.
b
Sublimates before melting.
c
Glass transition temperature given for polymers.
discussed as if it were simple cubic. In other words, the primitive unit—the smallest
repeating block—of the crystal lattice resembles a cube. The three major coordinate
axes of the cube are called the principal axes. Specific directions and planes within
the crystal are designated in reference to the principal axes using Miller indices [1], a
special notation from materials science that, in cubic crystals, includes three integers
with different surrounding “punctuation.” Directions are specified by brackets; for
example [100], which is a vector in the +x direction, referred to the three principal
axes (x,y,z) of the cube. No commas are used between the numbers, and negative
numbers have a bar over the number rather than a minus sign. Groups of directions

y, [010]
x, [100]
(110)
(110)
(111) = (111) (111) = (111)
(111) = (111) (111) = (111)
Figure 2.1 (a) Three crystallographic planes and their Miller indices for a simple cubic crystal.
Two planes in the {110} set of planes are identified. (b) The four planes in the {111} family. Note
that
()111
is the same plane as (111).
The determinants of plane and direction equivalence are the symmetry opera
-
tions that carry a crystal lattice (including the primitive unit) back into itself (i.e., the
transformed lattice after the symmetry operation is complete is identical to the start
-
ing lattice). With some thought, it becomes evident that 90º rotations and mirror
operations about the three principal axes are symmetry operations for a simple cubic
crystal. Therefore, the +x direction is equivalent to the +y direction under a 90º rota
-
tion; the +y direction is equivalent to the –y direction under a mirror operation, and
so forth. Hence, the +x,–x,+y,–y,+z, and –z directions are all equivalent. Vector
algebra (using a dot product) shows that the angles between {100} and {110} planes
are 45º or 90º, and the angles between {100} and {111} planes are 54.7º or 125.3º.
Similarly, {111} and {110} planes can intersect each other at 35.3º, 90º, or 144.7º.
The angle between {100} and {111} planes is of particular importance in
micromachining because many alkaline aqueous solutions, such as potassium
hydroxide (KOH), selectively etch the {100} planes of silicon but not the {111}
planes (discussed in detail in Chapter 3). The etch results in cavities that are bounded
by {111} planes (see Figure 2.2).

1. A (100) silicon wafer can be cleaved by scratching the surface with a sharp diamond scribe along a <110>
direction (parallel or perpendicular to the flat), clamping the wafer on one side of the scratch, and applying a
bending force to the free side of the wafer. Fracture occurs preferentially along <110> directions on the
surface. The newly exposed fracture surfaces tend to be {111} planes, which are sloped at 54.7° with respect
to the surface.
of impurity doping, but stresses tend to rise when dopant concentrations reach high
levels (~ 10
20
cm
−3
).
Polysilicon is an important material in the integrated circuit industry and has
been extensively studied. A detailed description of its electrical properties is found
in [2]. Polysilicon is an equally important and attractive material for MEMS. It
has been successfully used to make micromechanical structures and to integrate
electrical interconnects, thermocouples, p-n junction diodes, and many other elec
-
trical devices with micromechanical structures. The most notable example is the
acceleration sensor available from Analog Devices, Inc., of Norwood, Massachu
-
setts, for automotive airbag safety systems. Surface micromachining based on poly
-
silicon is today a well-established technology for forming thin (a few micrometers)
and planar devices.
The mechanical properties of polycrystalline and amorphous silicon vary with
deposition conditions, but, by and large, they are similar to that of single crystal sili
-
con [3]. Both normally have relatively high levels of intrinsic stress (hundreds of
MPa) after deposition, which requires annealing at elevated temperatures (>900ºC).
Silicon-Compatible Material System 17

Secondary flat
Secondary flat
(100) n-type
Primary flat
(100) p-type
Primary flat
No secondary flat
Secondary flat
Figure 2.2 (a) Illustration showing the primary and secondary flats of {100} and {111} wafers for
both n-type and p-type doping (SEMI standard); (b) illustration identifying various planes in a
wafer of {100} orientation (the wafer thickness is exaggerated); and (c) perspective view of a {100}
wafer and a KOH-etched pit bounded by {111} planes.
Beam structures made of polycrystalline or amorphous silicon that have not been
subjected to a careful stress annealing step can curl under the effect of intrinsic
stress.
Silicon is a very good thermal conductor with a thermal conductivity greater than
that of many metals and approximately 100 times larger than that of glass. In com
-
plex integrated systems, the silicon substrate can be used as an efficient heat sink.
This feature will be revisited when we review thermal-based sensors and actuators.
Unfortunately, silicon is not an active optical material—silicon-based lasers do
not exist. Because of the particular interactions between the crystal atoms and the
conduction electrons, silicon is effective only in detecting light; emission of light
is very difficult to achieve. At infrared wavelengths above 1.1 µm, silicon is
transparent, but at wavelengths shorter than 0.4 µm (in the blue and ultraviolet por
-
tions of the spectrum), it reflects over 60% of the incident light (see Figure 2.3). The
attenuation depth of light in silicon (the distance light travels before the intensity
drops to 36% of its initial value) is 2.7 µm at 633 nm (red) and 0.2 µm at 436 nm
(blue-violet). The slight attenuation of red light relative to other colors is what gives

20
30
40
50
60
70
80
90
100
0
0.5
1 1.5 2
Reflectivity (%)
Figure 2.3 Optical reflectivity for silicon and selected metals.
applications. For example, experiments have shown that silicon remains intact in
the presence of Freon™ gases as well as automotive fluids such as brake fluids.
Silicon has also proven to be a suitable material for applications such as valves
involving the delivery of ultra-high-purity gases. In medicine and biology, studies
are ongoing to evaluate silicon for medical implants. Preliminary medical evidence
indicates that silicon is benign in the body and does not release toxic sub-
stances when in contact with biological fluids; however, it appears from recent
experiments that bare silicon surfaces may not be suitable for high-performance
polymerase chain reactions (PCR) intended for the amplification of genetic DNA
material.
Silicon Oxide and Nitride
It is often argued that silicon is such a successful material because it has a stable
oxide that is electrically insulating—unlike germanium, whose oxide is soluble in
water, or gallium arsenide, whose oxide cannot be grown appreciably. Various
forms of silicon oxides (SiO
2

Coefficient of linear
expansion (10
−6
K
−1
)
–0,002.616 –0,003.253 –0,003.614 –93.842 –94.016
Specific heat (J/g·K) –0,000.713 –0,000.785 –0,000.832 –90.849 –90.866
Thermal conductivity
(W/cm·K)
–0,001.56 –0,001.05 –0,000.8 –90.64 –90.52
Temperature coefficient
of Young’s modulus (10
−6
K
−1
)
–0,–90 –0,–90 –0,–90 –90 –90
Temperature coefficient
of piezoresistance (10
−6
K
−1
)
(doping <10
18
cm
−3
)
–2,500 –2,500 –2,500 — —

ble, and gold excels in the infrared. Platinum and palladium are two very stable mate
-
rials for electrochemistry, though their fabrication entails some added complexity.
Gold, platinum, and iridium are good choices for microelectrodes, used in electro
-
chemistry and in sensing biopotentials. Silver is also useful in electrochemistry. Chro
-
mium, titanium, and titanium-tungsten are frequently used as very thin (5–20 nm)
adhesion layers for metals that have poor adhesion to silicon, silicon dioxide, and sili-
con nitride. Metal bilayers consisting of an adhesion layer (e.g., chromium) and an
20 Materials for MEMS
Table 2.3 List of Selected Metals That Can Be Deposited As Thin Films (Up to a Few µm in Thickness) with
Corresponding Electrical Resistivities and Typical Areas of Application
Metal ρ (µΩ·cm) Typical Areas of Application
Ag 1.58 Electrochemistry
Al 2.7 Electrical interconnects; optical reflection in the visible
and the infrared
Au 2.4 High-temperature electrical interconnects; optical
reflection in the infrared; electrochemistry;
corrosion-resistant contact; wetting layer for soldering
Cr 12.9 Intermediate adhesion layer
Cu 1.7 Low-resistivity electrical interconnects
Indium-tin oxide (ITO) 300–3,000 Transparent conductive layer for liquid crystal displays
Ir 5.1 Electrochemistry; microelectrodes for sensing biopotentials
Ni 6.8 Magnetic transducing; solderable layer
NiCr 200–500 Thin-film laser trimmed resistor; heating element
Pd 10.8 Electrochemistry; solder-wetting layer
Permalloy™ (Ni
x
Fe

humidity [7].
Other Materials and Substrates
Over the years, micromachining methods have been applied to a variety of sub-
strates to fabricate passive microstructures as well as transducers. Fabrication
processes for glass and quartz are mature and well established, but for other materi-
als, such as silicon carbide, new techniques are being explored and developed. In the
process, these activities add breadth to micromachining technology and enrich the
inventory of available tools. The following sections briefly review the use of a few
materials other than silicon.
Glass and Fused Quartz Substrates
Glass is without a doubt a companion material to silicon; the two are bonded
together figuratively and literally in many ways. Silicon originates from processed
and purified silicates (a form of glass), and silicon can be made to bond electrostati
-
cally to Pyrex
®
glass substrates—a process called anodic bonding and common in
the making of pressure sensors. But like all relatives, differences remain. Glasses
generally have different coefficients of thermal expansion than silicon (fused quartz
is lower, while window glass is higher), resulting in interfacial stresses between
bonded silicon and glass substrates.
Micromachining of glass and fused quartz (amorphous silicon dioxide) sub
-
strates is practical in special applications, such as when an optically transparent or
an electrically insulating substrate is required. Crystalline quartz (as opposed to
fused quartz) also has the distinct property of being piezoelectric and is used for
some MEMS devices. However, micromachining of glass or quartz is limited in
scope relative to silicon. Etching in HF or ultrasonic drilling typically yields coarsely
defined features with poor edge control. Thin metal films can be readily deposited
on glass or quartz substrates and defined using standard lithographic techniques.

Diamond has an extremely high ratio of Young’s modulus to density, giving vibrat-
ing structures made of diamond higher resonant frequencies than similar structures
made of other materials. In addition to the properties listed earlier, diamond films
are also good field emitters and have received extensive study as a source of elec
-
trons for such applications as displays. Etching diamond films is even more difficult
than for silicon carbide, so alternative patterning methods such as selective deposi
-
tion are used [9].
Gallium Arsenide and Other Group III-V Compound Semiconductors
Rather than ponder the utility of gallium arsenide (GaAs) and other group III-V
compounds (e.g., InP, AlGaAs, GaN) as alternate substrate materials to silicon, it is
perhaps more appropriate to think of micromachining as a set of tools that can pro
-
vide solutions to issues specific to devices that currently can only be built in these
materials, in particular lasers and optical devices. In that regard, micromachining
becomes an application-specific toolbox whose main characteristic is to address
ways to enable new functions or enhance existing ones.
Micromechanical structures such as springs and bridges have been formed in
GaAs by both reactive ion etching [10] and orientation-dependent etching [11] (dis
-
cussed in Chapter 3). Micromachining has also been used to incorporate structures
such as mirrors on the surface of III-V semiconductors to create new devices, includ
-
ing tunable lasers [12]. Moreover, micromachining using GaAs and other group
22 Materials for MEMS
III-V compound semiconductors is a practical way to integrate RF switches, anten
-
nas, and other custom high-frequency components with ultra-high-speed electronic
devices for wireless telecommunications.

[14]. In the electronics industry, polyimide has been used as a flexible substrate for
printed circuit boards and for hard disk drives. In micromachining, sheets have been
laser cut to form microfluidic devices, while spin-on films have been used as resists,
sacrificial layers, and a wafer-bonding adhesive.
Other polymers finding application in MEMS include parylenes and silicones.
Parylenes are deposited by chemical-vapor deposition to form a conformal coating.
There are several forms of parylene due to variations in the chemical structure [15].
Like polyimide, parylenes are fairly inert chemically and form a barrier to the flow
of water and other vapors. Silicones are different from most other polymers in that
the backbone chain of atoms is silicon rather than carbon. Silicones are very compli
-
ant and have been used as the deformable membrane in valves [15], as well as being
a common die-attach material in packaging (see Chapter 8).
Shape-Memory Alloys
The shape-memory effect is a unique property of a special class of alloys that return
to a predetermined shape when heated above a critical transition temperature. The
Other Materials and Substrates 23
material “remembers” its original shape after being strained and deformed. The dis
-
covery was first made in a gold-cadmium alloy in 1951 but was quickly extended to
a broad range of other alloys, including titanium-nickel, copper-aluminum-nickel,
iron-nickel and iron-platinum alloys. A basic understanding of the underlying physi
-
cal principles was established in the 1970s, but extensive research remains ongoing
in an effort to develop a thorough theoretical foundation. Nonetheless, the potential
applications for shape-memory alloys abound. It has been estimated that upwards of
15,000 patents have been applied for on this topic. Titanium-nickel alloys have been
the most widely used of shape-memory alloys because of their relative simple com
-
position and robustness.

Piezoresistivity is a widely used physical effect and has its name derived from the
Greek word piezein meaning to apply pressure. Discovered first by Lord Kelvin in
1856, it is the phenomenon by which an electrical resistance changes in response to
mechanical stress. The first application of the piezoresistive effect was metal strain
gauges to measure strain, from which other parameters such as force, weight, and
pressure were inferred (see Figure 2.4). Most the resistance change in metals is due to
24 Materials for MEMS
dimensional changes: under stress, the resistor gets longer, narrower, and thinner
[17]. C. S. Smith’s discovery in 1954 [18] that the piezoresistive effect in silicon
and germanium was much greater (by roughly two orders of magnitude) than in
metals spurred significant interest. The first pressure sensors based on diffused
(impurity-doped) resistors in thin silicon diaphragms were demonstrated in 1969
[19]. The majority of today’s commercially available pressure sensors use silicon
piezoresistors.
For the physicist at heart, piezoresistivity arises from the deformation of the
energy bands as a result of an applied stress. In turn, the deformed bands affect the
effective mass and the mobility of electrons and holes, hence modifying resistivity.
For the engineer at heart, the fractional change in resistivity, ∆ρ/ρ, is to a first order
linearly dependent on σ
//
and σ
⊥
, the two stress components parallel and orthogonal
to the direction of the resistor, respectively. The direction of the resistor is here
defined as that of the current flow. The relationship can be expressed as
∆ρ ρ π σ π σ
// //
=+
⊥⊥
where the proportionality constants, π

2. The gauge factor, K, is the constant of proportionality relating the fractional change in resistance, ∆R/R,to
the applied strain, ε, by the relationship ∆R/R = K⋅ε.
way to incorporate stress-independent diffused temperature sensors. The crystal-
orientation-dependence of the piezoresistive coefficients takes a more complex func
-
tion for piezoresistors diffused in {110} wafers, but this dependence fortuitously dis
-
appears in {111} wafers. More descriptive details of the underlying physics of
piezoresistivity and dependence on crystal orientation can be found in [20, 21].
If we consider p-type piezoresistors diffused in {100} wafers and oriented in the
<110> direction (parallel or perpendicular to the flat), it is apparent from the posi
-
tive sign of π
//
in Table 2.4 that the resistance increases with tensile stress applied in
the parallel direction, σ
//
, as if the piezoresistor itself is being elongated. Further
-
more, the negative sign of π
⊥
implies a decrease in resistance with tensile stress
orthogonal to the resistor, as if its width is being stretched. In actuality, the stretch
-
ing or contraction of the resistor are not the cause of the piezoresistive effect, but
they make a fortuitous analogy to readily visualize the effect of stress on resistance.
This analogy breaks down for n-type piezoresistors.
Like many other physical effects, piezoresistivity is a strong function of tempera
-
ture. For lightly doped silicon (n-orp-type, 10

−3
, the TCR for
polycrystalline silicon is approximately 0.04% per degree Celsius compared to
0.14% per degree Celsius for crystalline silicon. The deposition process and the
dopant species have been found to even alter the sign of the TCR. For example,
emitter-type polysilicon (a special process for depositing heavily doped polysilicon
to be used as emitter for bipolar transistors) has a TCR of –0.045% per degree Cel
-
sius. Resistors with positive TCR are particularly useful in compensating the nega
-
tive temperature dependence of piezoresistive sensors.
Piezoelectricity
Certain classes of crystals exhibit the peculiar property of producing an electric field
when subjected to an external force. Conversely, they expand or contract in response
26 Materials for MEMS
Table 2.4 Piezoresistive Coefficients for n- and p-Type {100}
Wafers and Doping Levels Below 10
18
cm
-3
π
//
(10
-11
m
2
/N)
π
⊥
(10

zero only in the absence of an externally applied stress. Straining the crystal shifts
the relative positions of the positive and negative charges, giving rise to an electric
dipole within the primitive unit and a net polarization across the crystal. Con-
versely, the internal electric dipoles realign themselves in response to an externally
applied electric field, causing the atoms to displace and resulting in a measurable
crystal deformation. When the temperature exceeds a critical value called the Curie
temperature, the material loses its piezoelectric characteristics.
The piezoelectric effect is described in terms of piezoelectric charge coefficients,
d
ij
, which relate the static voltage, electric field, or surface charge in the i direction to
displacement, applied force, or stress in the j direction. The convention for describ
-
ing piezoelectrics is that the direction of polarization is the “3” or z direction of the
crystal axis, while a direction perpendicular to it is the “1” or x or y direction of the
crystal. Hence, piezoelectric charge coefficients are given as d
33
for both voltage and
Important Material Properties and Physical Effects 27
p
i
p
i
Σp=0
i
Σ≠p0
i
Figure 2.5 Illustration of the piezoelectric effect in a hypothetical two-dimensional crystal. The
net electric dipole within the primitive unit of an ionic crystal lacking a center of symmetry does
not vanish when external stress is applied. This is the physical origin of piezoelectricity. (After:

Width (W)
Length (L)
Thickness (t)
2
1
3 (Direction of polarization)
V
Figure 2.7 An illustration of the piezoelectric effect on a crystalline plate. An applied voltage
across the electrodes results in dimensional changes in all three axes (if d
31
and d
33
are nonzero).
Conversely, an applied force in any of three directions gives rise to a measurable voltage across the
electrodes.
p
i
p
i
Σp=0
i
Σp0
i
=
Figure 2.6 Illustration of the vanishing dipole in a two-dimensional lattice. A crystal possessing a
center of symmetry is not piezoelectric because the dipoles, p
i
, within the primitive unit always
cancel each other out. Hence, there is no net polarization within the crystal. An externally applied
stress does not alter the center of symmetry. (After: [21].)

put in place until early in the twentieth century by Boltzmann. In the absence of a
magnetic field, there are three distinct thermoelectric effects: the Seebeck, the Pel-
tier, and the Thomson effects [25]. The Seebeck effect is the most frequently used
(e.g., in thermocouples for the measurement of temperature differences). The Peltier
effect is used to make thermoelectric coolers (TECs) and refrigerators. The Thom-
son effect is less known and uncommon in daily applications.
In the Peltier effect, current flow across a junction of two dissimilar materials
causes a heat flux, thus cooling one side and heating the other. Mobile wet bars with
Peltier refrigerators were touted in 1950s as the newest innovation in home appli
-
ances, but their economic viability was quickly jeopardized by the poor energy con
-
version efficiency. Today, Peltier devices are made of n-type and p-type bismuth
telluride elements and are used to cool high-performance microprocessors, laser
diodes, and infrared sensors. Peltier devices have proven to be difficult to implement
as micromachined thin-film structures.
Important Material Properties and Physical Effects 29
Table 2.5 Piezoelectric Coefficients and Other Relevant Properties for a Selected List of Piezoelectric
Materials
Material Piezoelectric
Constant (d
ijj
)
(10
−12
C/N)
Relative
Permittivity
(ε
rr

31
=−4, d
33
= 23 28 4.6 245 34
BaTiO3 d
31
= 78, d
33
= 190 1,700 5.7 30
PZT d
31
=−171 d
33
= 370 1,700 7.7 53 30
zinc oxide (ZnO) d
31
= 5.2, d
33
= 246 1,400 5.7 123 33